Solved on Dec 13, 2023

Compare ride capacity: 25 race cars in 30 min vs 20 spin swings in 20 min. Which has higher hourly capacity?

STEP 1

Assumptions
1. 25 riders ride the race cars every 30 minutes.
2. 20 riders ride the spin swings every 20 minutes.
3. We are comparing the number of riders for each ride in one hour.
4. The number of riders is directly proportional to the time.

STEP 2

First, we need to calculate the number of riders for the race cars in one hour. Since 25 riders ride every 30 minutes, we can multiply this number by 2 to find the hourly rate.
$Riders_{race\, cars\, per\, hour} = Riders_{race\, cars\, per\, 30\, minutes} \times 2$

STEP 3

Now, plug in the given values for the race cars to calculate the hourly rate.
$Riders_{race\, cars\, per\, hour} = 25 \times 2$

STEP 4

Calculate the number of riders for the race cars per hour.
$Riders_{race\, cars\, per\, hour} = 25 \times 2 = 50$

STEP 5

Next, we need to calculate the number of riders for the spin swings in one hour. Since 20 riders ride every 20 minutes, we can find the hourly rate by calculating how many 20-minute intervals there are in one hour and multiplying the number of riders by this factor.
$Riders_{spin\, swings\, per\, hour} = Riders_{spin\, swings\, per\, 20\, minutes} \times \frac{60}{20}$

STEP 6

Now, plug in the given values for the spin swings to calculate the hourly rate.
$Riders_{spin\, swings\, per\, hour} = 20 \times \frac{60}{20}$

STEP 7

Calculate the number of riders for the spin swings per hour.
$Riders_{spin\, swings\, per\, hour} = 20 \times 3 = 60$

STEP 8

Now that we have the number of riders per hour for both rides, we can compare them to see which ride has more riders each hour.
$Riders_{race\, cars\, per\, hour} = 50$ $Riders_{spin\, swings\, per\, hour} = 60$

STEP 9

Determine which ride has more riders and by how many.
$More\, riders = Riders_{spin\, swings\, per\, hour} - Riders_{race\, cars\, per\, hour}$

STEP 10

Plug in the values to calculate the difference in the number of riders.
$More\, riders = 60 - 50$

STEP 11

Calculate the difference in the number of riders.
$More\, riders = 60 - 50 = 10$
The spin swings will have 10 more riders each hour compared to the race cars.

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Compare ride capacity: 25 race cars in 30 min vs 20 spin swings in 20 min. Which has higher hourly capacity?

STEP 1

Assumptions
1. 25 riders ride the race cars every 30 minutes.
2. 20 riders ride the spin swings every 20 minutes.
3. We are comparing the number of riders for each ride in one hour.
4. The number of riders is directly proportional to the time.

STEP 2

First, we need to calculate the number of riders for the race cars in one hour. Since 25 riders ride every 30 minutes, we can multiply this number by 2 to find the hourly rate.
$Riders_{race\, cars\, per\, hour} = Riders_{race\, cars\, per\, 30\, minutes} \times 2$

STEP 3

Now, plug in the given values for the race cars to calculate the hourly rate.
$Riders_{race\, cars\, per\, hour} = 25 \times 2$

STEP 4

Calculate the number of riders for the race cars per hour.
$Riders_{race\, cars\, per\, hour} = 25 \times 2 = 50$

STEP 5

STEP 6

Now, plug in the given values for the spin swings to calculate the hourly rate.
$Riders_{spin\, swings\, per\, hour} = 20 \times \frac{60}{20}$

STEP 7

Calculate the number of riders for the spin swings per hour.
$Riders_{spin\, swings\, per\, hour} = 20 \times 3 = 60$

STEP 8

Now that we have the number of riders per hour for both rides, we can compare them to see which ride has more riders each hour.
$Riders_{race\, cars\, per\, hour} = 50$ $Riders_{spin\, swings\, per\, hour} = 60$

STEP 9

Determine which ride has more riders and by how many.
$More\, riders = Riders_{spin\, swings\, per\, hour} - Riders_{race\, cars\, per\, hour}$

STEP 10

Plug in the values to calculate the difference in the number of riders.
$More\, riders = 60 - 50$

STEP 11

Calculate the difference in the number of riders.
$More\, riders = 60 - 50 = 10$
The spin swings will have 10 more riders each hour compared to the race cars.

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Compare ride capacity: 25 race cars in 30 min vs 20 spin swings in 20 min. Which has higher hourly capacity?

STEP 1

Assumptions1. 25 riders ride the race cars every 30 minutes.2. 20 riders ride the spin swings every 20 minutes.3. We are comparing the number of riders for each ride in one hour.4. The number of riders is directly proportional to the time.

STEP 2

STEP 3

Now, plug in the given values for the race cars to calculate the hourly rate.Ridersrace cars per hour=25×2Riders_{race\, cars\, per\, hour} = 25 \times 2Ridersracecarsperhour​=25×2

STEP 4

Calculate the number of riders for the race cars per hour.Ridersrace cars per hour=25×2=50Riders_{race\, cars\, per\, hour} = 25 \times 2 = 50Ridersracecarsperhour​=25×2=50

STEP 5

STEP 6

Now, plug in the given values for the spin swings to calculate the hourly rate.Ridersspin swings per hour=20×6020Riders_{spin\, swings\, per\, hour} = 20 \times \frac{60}{20}Ridersspinswingsperhour​=20×2060​

STEP 7

Calculate the number of riders for the spin swings per hour.Ridersspin swings per hour=20×3=60Riders_{spin\, swings\, per\, hour} = 20 \times 3 = 60Ridersspinswingsperhour​=20×3=60

STEP 8

STEP 9

Determine which ride has more riders and by how many.More riders=Ridersspin swings per hour−Ridersrace cars per hourMore\, riders = Riders_{spin\, swings\, per\, hour} - Riders_{race\, cars\, per\, hour}Moreriders=Ridersspinswingsperhour​−Ridersracecarsperhour​

STEP 10

Plug in the values to calculate the difference in the number of riders.More riders=60−50More\, riders = 60 - 50Moreriders=60−50

STEP 11

Calculate the difference in the number of riders.More riders=60−50=10More\, riders = 60 - 50 = 10Moreriders=60−50=10The spin swings will have 10 more riders each hour compared to the race cars.

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Assumptions
1. 25 riders ride the race cars every 30 minutes.
2. 20 riders ride the spin swings every 20 minutes.
3. We are comparing the number of riders for each ride in one hour.
4. The number of riders is directly proportional to the time.

Now, plug in the given values for the race cars to calculate the hourly rate.
$Riders_{race\, cars\, per\, hour} = 25 \times 2$

Calculate the number of riders for the race cars per hour.
$Riders_{race\, cars\, per\, hour} = 25 \times 2 = 50$

Now, plug in the given values for the spin swings to calculate the hourly rate.
$Riders_{spin\, swings\, per\, hour} = 20 \times \frac{60}{20}$

Calculate the number of riders for the spin swings per hour.
$Riders_{spin\, swings\, per\, hour} = 20 \times 3 = 60$

Determine which ride has more riders and by how many.
$More\, riders = Riders_{spin\, swings\, per\, hour} - Riders_{race\, cars\, per\, hour}$

Plug in the values to calculate the difference in the number of riders.
$More\, riders = 60 - 50$

Calculate the difference in the number of riders.
$More\, riders = 60 - 50 = 10$
The spin swings will have 10 more riders each hour compared to the race cars.